Notice that 25 p^2 - 144 is what is called a "difference of squares", because 25 = 5^2 , p^2 is the square of "p", and 144 is the same as 12^2
Then we use the factoring form for a difference of squares given by:
a^2 - b^2 = ( a - b) (a + b)
with in our case: a = 5 p, and b = 12
so we have:
25 p^2 - 144 = (5 p)^2 - (12)^2 = (5p - 12) (5 p + 12)
We need to factor the expression:
- 2 x^2 + 32
so we proceed to extract all common factors (this time there are only numerical factors: "2" is the only one .
2 (- x^2 + 16) = 2 (16 - x^2)
notice now that the expression in parenthesis is a "difference of squares" that can be factored using the factor form be used above. Then we end up with the following factors:
2 (4 - x) (4 + x)
since 16 = 4^2 and x^2 is the square of "x".